Let \(m\)  be a positive integer, \(r\)  a power of a prime, and \(\mathbb {F}_r\)  the finite field with \(r\)  elements. The polynomial \(x^m-1\in \mathbb {F}_r[x]\)  has no repeated factors (which are irreducible over \(\mathbb {F}_r\) ) if and only if \(r\)  and \(m\)  are relatively prime, i.e. \(gcd(r,m)=1\) 
(see [1]}), which we assume in this section.
